# Ch 16: Geometry and Trigonometry - AP Calculus: Homeschool Curriculum

### About This Chapter

## Who's it for?

This unit of our AP Calculus Homeschool course will benefit any student who is trying to learn about geometry and trigonometry. There is no faster or easier way to learn about calculus. Among those who would benefit are:

- Students who require an efficient, self-paced course of study to learn to visualize geometry problems using hands-on and graphical approaches.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a calculus curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.

## How it works:

- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a Geometry and Trigonometry unit exam confirm understanding or identify any topics that require review.

## Geometry and Trigonometry Unit Objectives:

- Use the Pythagorean Theorem to find distance.
- Learn to graph sines and cosines.
- Use the Pythagorean Theorem to go between right triangles and trigonometry.
- Calculate the volume of pyramids, spheres and other shapes.

### 1. How to Solve Visualizing Geometry Problems

Visualizing geometry problems involves knowing the expected results, and identifying the important pieces of information to make sure all the mathematical details match the word problem. See several examples of how to solve these problems correctly.

### 2. How to Calculate the Volumes of Basic Shapes

The basic formula for volume is length * width * height and is necessary in geometry and the science of understanding mass in the form of basic shapes. Learn more about how to calculate the volumes of basic shapes and use the methodologies.

### 3. Finding Distance with the Pythagorean Theorem

The Pythagorean theorem outlines principles for right triangles, but it can also be used to calculate distance between points. Learn how this theorem is applied to practical examples of ice cream, skateboard ramps, and even the cliff-peak in 'The Lion King.'

### 4. Trigonometry: Sine and Cosine

Sine and cosine are basic trigonometric functions that are used to solve for the angles and sides of triangles. Review trigonometry concepts and learn about the mnemonic used for sine, cosine, and tangent functions.

### 5. Trigonometry and the Pythagorean Theorem

The SohCahToa and the Pythagorean Theorem are two rules for finding equations in trigonometry. Learn more about the definitions of the SohCahToa and the Pythagorean Theorem, understand how they work, and how to use them in calculus.

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### Other Chapters

Other chapters within the AP Calculus AB & BC: Homeschool Curriculum course

- Functions - AP Calculus: Homeschool Curriculum
- Graphing & Functions - AP Calculus: Homeschool Curriculum
- Sequences & Series - AP Calculus: Homeschool Curriculum
- Limits - AP Calculus: Homeschool Curriculum
- Continuity - AP Calculus: Homeschool Curriculum
- Exponentials & Logarithms: Homeschool Curriculum
- Exponents & Polynomials - AP Calculus: Homeschool Curriculum
- Applications of Derivatives - AP Calculus: Homeschool Curriculum
- Calculating Derivatives & Derivative Rules - AP Calculus: Homeschool Curriculum
- Differential Equations - AP Calculus: Homeschool Curriculum
- Area Under the Curve & Integrals - AP Calculus: Homeschool Curriculum
- Graphing Derivatives & L'Hopital's Rule - AP Calculus: Homeschool Curriculum
- Integration & Integration Techniques - AP Calculus: Homeschool Curriculum
- Integration Applications - AP Calculus: Homeschool Curriculum
- Rate of Change - AP Calculus: Homeschool Curriculum
- Using Scientific Calculators - AP Calculus: Homeschool Curriculum